Water-bag stability theory for planar bounded plasmas with counter-streaming injection. Part 1. The neutralized diode

Abstract

The stability of a bounded, homogeneous, neutralized plasma with counter- streaming electron beams is analysed. A water-bag model is used to describe the electron distribution in velocity space, so that finite beam temperature and a background plasma are included in the theory. For boundary conditions, the absorber– source wall (the diode boundary) and the reflecting wall are considered. For the former, growth-rate calculations indicate that the instability is a combination of charge bunching (counter-streaming) and diode circuit effect. As the diode length increases, the growth rate of all modes in the system approaches the maximum growth rate. For the reflecting wall, as the length increases, the maximum growth rate transfers to higher and higher order modes with shorter wavelength, while the growth rate of the lower-order modes goes to zero.